# The gravity equation and the interdependency of trade costs and international trade [Elektronische Ressource] / Stephan Rudolph

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The Gravity Equation and theInterdependency of Trade Costs andInternational TradeDoctoral DissertationStephan RudolphFaculty of Business Management and EconomicsTechnische Universit at DresdenReferees: Prof. Dr. Udo Broll, Prof. Dr. Georg HirteJanuary 10, 2011Contents1 Introduction 12 The Gravity Equation: Theory and Application 82.1 Theoretical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.1 Demand Side Models . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.2 A Supply Side Model . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1.3 Gravity Equations Derived from New-new Trade Theory . . . . . . 172.2 Empirical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.1 The Basic Speci cation . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.2 Dealing with Unobservable Country Characteristics: Fixed E ects . 202.2.3 Dealing with Zero-Trade-Flows: Non-linear Estimators . . . . . . . 232.2.4 Dealing with Endogeneity and Simultaneity: Instrumental Variables 252.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 A Theory of Endogenous Trade Costs 28ICONTENTS3.1 A Theory Based Gravity Equation . . . . . . . . . . . . . . . . . . . . . . 313.2 A Micro-founded Form of Trade Costs . . . . . . . . . . . . . . . . . . . . 363.3 Economies of Scale in International Commodity Trade . . . . . . . . . . . 373.

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The Gravity Equation and the
Doctoral Dissertation
Stephan Rudolph
Faculty of Business Management and Economics
Technische Universit at Dresden
Referees: Prof. Dr. Udo Broll, Prof. Dr. Georg Hirte
January 10, 2011Contents
1 Introduction 1
2 The Gravity Equation: Theory and Application 8
2.1 Theoretical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Demand Side Models . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 A Supply Side Model . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 Gravity Equations Derived from New-new Trade Theory . . . . . . 17
2.2 Empirical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 The Basic Speci cation . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Dealing with Unobservable Country Characteristics: Fixed E ects . 20
2.2.3 Dealing with Zero-Trade-Flows: Non-linear Estimators . . . . . . . 23
2.2.4 Dealing with Endogeneity and Simultaneity: Instrumental Variables 25
2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 A Theory of Endogenous Trade Costs 28
ICONTENTS
3.1 A Theory Based Gravity Equation . . . . . . . . . . . . . . . . . . . . . . 31
3.2 A Micro-founded Form of Trade Costs . . . . . . . . . . . . . . . . . . . . 36
3.3 Economies of Scale in International Commodity Trade . . . . . . . . . . . 37
3.4 Interaction between the Gravity Equation and Trade Cost Function . . . . 40
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Estimation 45
4.1 Econometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5 Computing Multilateral Resistances 63
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Computing Bilateral Trade Costs . . . . . . . . . . . . . . . . . . . . . . . 67
5.3 Computing the Multilateral Resistances . . . . . . . . . . . . . . . . . . . . 68
5.3.1 The Equation System and its Solution . . . . . . . . . . . . . . . . 68
5.3.2 An Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3.3 Multilateral Resistances of the 23 OECD Countries . . . . . . . . . 76
IICONTENTS
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6 Estimation with Multilateral Resistances 84
6.1 Econometric Model and Data . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7 Summary 94
A Derivation of the Gravity Equation (Anderson and van Wincoop) 100
B Derivation of the Index for Bilateral Trade Costs 104
C Multilateral Resistances as a Linear Equation System 106
Bibliography 108
IIIList of Figures
1.1 Regional Structure of the World Trade . . . . . . . . . . . . . . . . . . . . 3
1.2 Organization of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Distribution of Country Pairs Based on Direction of Trade . . . . . . . . . 24
3.1 Plot of the Bias Term with a Given Value for the Elasticity of Substitution 42
4.1 Trade Cost Index of Germany . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Residual-Analysis of the Standard Gravity Speci cation . . . . . . . . . . . 55
4.3 of the Theory-Based Gravity Equation . . . . . . . . . . 60
4.4 Residual-Analysis of the Theory-Based Trade Cost Equation . . . . . . . . 60
5.1 Simulation Results of the Three Country Example (Upward Approximation) 76
5.2 Simulation Results of the Three Country Example (Downward Approxi-
mation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3 Countries with Low Multilateral Resistances . . . . . . . . . . . . . . . . . 81
IVLIST OF FIGURES
5.4 Countries with High Multilateral Resistances . . . . . . . . . . . . . . . . . 81
5.5 Multilateral Resistances of Australia, Japan, Korea, and the U.S. . . . . . 82
6.1 Residual-Analysis of the Standard Gravity Speci cation . . . . . . . . . . . 90
6.2 of the Standard Gravity Speci cation . . . . . . . . . . . 90
VList of Tables
4.1 Summary statistics of the OECD data set . . . . . . . . . . . . . . . . . . 54
4.2 Results of the Standard Speci cation . . . . . . . . . . . . . . . . . . . . . 56
4.3 Results of the Speci cation with Trade Cost Endogeneity . . . . . . . . . . 57
5.1 Assumed Data for the Numerical Example . . . . . . . . . . . . . . . . . . 72
5.2 Simulation of the Numerical Example . . . . . . . . . . . . . . . . . . . . . 75
5.3 Amplitude and Convergence of the Simulation . . . . . . . . . . . . . . . . 78
5.4 Descriptive statistics of =P P . . . . . . . . . . . . . . . . . 781 i(100) i(99)
5.5 Summary statistics of the Multilateral Resistances . . . . . . . . . . . . . . 80
6.1 Summary statistics of the OECD data set . . . . . . . . . . . . . . . . . . 86
6.2 Results of the Standard Speci cation . . . . . . . . . . . . . . . . . . . . . 89
6.3 Results of the Simultaneous Equation Model . . . . . . . . . . . . . . . . . 91
VIChapter 1
Introduction
11. Introduction
The gravity equation is probably the most important tool in international economics to
explain and estimate trade ows. In its simplest form, it states that the exports between
any two given countries (say i and j) are a multiplicative function of these countries’
economic size, as measured by GDP, and their bilateral trade costs:
GDP GDPi j
Exports = : (1.1)ij Trade Costsij
The idea goes back to the pioneering works of Tinbergen (1962) and P oyh onen (1963),
who developed gravity equations independently of each other. The name comes from the
similarity of equation (1.1) to Isaac Newton’s law of gravity where the attraction force
between two physical bodies equals the product of their masses divided by the squared
1distance between the bodies.
Figure 1.1 illustrates the idea behind the gravity equation with some data. It plots
the export values among world regions. For example, the tallest column in the corner
symbolizes the exports from European countries to European countries. With a value of
2\$4,243 billion (USD) they account for one third of world trade. On the one hand, it
can be seen from this gure that trade activities within regions that contain relatively
large economies (Europe, Asia and North America) are very high. On the other hand,
regions with rich countries seem to attract trade with regions containing poor countries.
For example, the trade between Europe and Africa is higher than the trade inside Africa.
Thus, there are obviously two contrary e ects on trade:
economic size increases trade ows and
1 The explicit formulation of Newton’s physical gravity equation to explain the attraction force between
two bodies i and j is:
Mass Massi j
Attraction Force = :ij 2Distanceij
2 Europe has a much higher export value than North America because it consists of multiple large
economies. For North America the USA is treated as one unit. If the individual, American states were
treated separately, such that \interstate trade" were recognized, the value for North exports
might be closer in magnitude to that of Europe.
21. Introduction
Exports (in billion US-\$)
4500
4000
3500
3000
2500
2000
1500
1000
500
0
tofrom
Figure 1.1: Regional Structure of the World Trade.
Source: WTO International Trade Statistics (2008).
3
Europe
Asia
North America
Latin America
Middle East
Africa
Africa
Middle East
Latin America
North America
Asia
Europe

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